Question

Three fair dice are thrown simultaneously. What is the probability that the sum is 5?

• A. 1/36
• B. 1/6
• C. 1/54
• D. 1/72

Hint:

For probability problems with dice, first calculate the total possible outcomes, then count the favorable outcomes to find the probability.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
We are asked to find the probability that the sum of the numbers rolled on three fair dice is 5.
Step 2: Total possible outcomes.
Each die has 6 faces, so the total number of possible outcomes when three dice are thrown is \(6 \times 6 \times 6 = 216\).
Step 3: Finding favorable outcomes.
To get a sum of 5, the following combinations of dice rolls are possible: (1, 1, 3), (1, 2, 2), (2, 1, 2), (3, 1, 1). There are 6 different combinations that add up to 5.
Step 4: Probability calculation.
The probability is the number of favorable outcomes divided by the total number of outcomes: \[ P(\text{sum of 5}) = \frac{6}{216} = \frac{1}{36}. \] Step 5: Conclusion.
The correct answer is (A) 1/36, which is the probability that the sum of the dice is 5.